Slope Ratio Method

In the slope-ratio method two sets of solutions are prepared. The first set consists of a constant amount of metal and a variable amount of ligand, chosen such that the total concentration of metal, Cm, is much greater than the total concentration of ligand. Cl- Under these conditions we may assume that essentially all the ligand is complexed. The concentration of a metal-ligand complex of the general... 

An important assumption in the slope-ratio method is that the complexation reaction continues to completion in the presence of a sufficiently large excess of metal or ligand. The slope-ratio method also is limited to systems that obey Beer s law and in which only a single complex is formed. 

Duboisia samples have been analysed for scopolamine and hyoscyamine, using g.l.c. by a slope ratio method and by methods employing homatropine, tetraphenyl-ethylene, and phenylacetyltropine as internal standards. The alkaloids were converted into their trimethylsilyl ethers with hexamethyldisilazane scopolamine was the major component, followed by hyoscyamine and norhyoscyamine, meteloidine, phenylacetyltropeine, and valeroidine, tigloidine, valtropine, butropine, and acetyl-tropine, together with some anabasine and nicotine as non-tropane bases. 

The three most common techniques used for complex-ion studies are (1) the method of continuous variations, (2) the mole-ratio method, and (3) the slope-ratio method. 

There are different methods to determine the stoichiometry, e.g. Continuous Variation Methods [6], the Slope Ratio Method [7], the Mole Ratio Method [8], and others. Because the Continuous Variation Method is the most popular among these, this method is adopted here to determine the stoichiometry. 

The different methods to determine the stoichiometry of a chemical reaction include continuous variation methods," the slope ratio method, - the mole ratio method, and others. Here we adopt the continuous variation method to determine the stoichiometry since it is the most widely employed method by the community. To determine the stoichiometry of a reaction by the continuous variation method, the following four points must be considered and carried out ... 

Slope ratio method— This is a modification of the nitrogen balance index wherein various levels of protein are fed adlibitum to growing animals. Then growth rate and protein intake are plotted on a graph, and the slope of this line is taken as the measure of protein quality. 

It has been suggested by Wood (53) that, for those microbiological assays which show a strictly linear portion to the standard curve, the so-called slope-ratio method diould be used for calculating the results. This method, of course, has the merit of being statistically sound, and it also has the valuable advantage that it is possible to calculate the fiducial limits of an assay. 

Unfortunately, the slope-ratio method of calculation has only a very restricted use in the computation of microbiological assay values. It is the exception rather than the rule that the mean response to a tube assay is linearly related to the dose, i. e., that there is a strictly linear portion of the standard curve. In the vast majority of assays, there is no linear portion of the standard curve which is curvilinear throughout its length. 

Both the method of continuous variations and the mole-ratio method rely on an extrapolation of absorbance data collected under conditions in which a linear relationship exists between absorbance and the relative amounts of metal and ligand. When a metal-ligand complex is very weak, a plot of absorbance versus Ay or n-J m may be curved, making it impossible to determine the stoichiometry by extrapolation. In this case the slope ratio may be used. 

In the mole-ratio method, a series of solutions is prepared in which the analytical concentration of one reactant (usually the cation) is held constant while that of the other is varied. A plot of absorbance versus mole ratio of the reactants is then made. If the formation constant is reasonably favorable, we obtain two straight lines of different slopes that intersect at a mole ratio corresponding to the combining ratio in the complex. Typical mole-ratio plots are shown in Figure 26-15. Notice that the ligand of the 1 2 complex absorbs at the wavelength selected so that the slope beyond the equivalence point is greater than zero. We deduce that the uncomplexed... 

Animal studies. In the initial studies (.6), a partially purified monoferric phytate prepared from extracts of wheat bran and two synthetic preparations were bioassayed using rats. The hemoglobin depletion-repletion method was used and the relative biological value (RBV) was computed by slope ratio. Compared to the response to ferrous ammonium sulfate as 100, the RBV for the monoferric phytate prepared from wheat bran was 99, and for the two synthetic preparations 101 and 97. The 95 confidence interval for the preparation from wheat bran was 87-111. The iron of monoferric phytate is highly bioavailable to rats. 

Raman spectroscopy is a scattering, not an absorption technique as FTIR. Thus, the ratio method cannot be used to determine the amount of light scattered unless an internal standard method is adopted. The internal standard method requires adding a known amount of a known component to each unknown sample. This known component should be chemically stable, not interact with other components in the sample and also have a unique peak. Plotting the Raman intensity of known component peaks versus known concentration in the sample, the proportional factor of Raman intensity to concentration can be identified as the slope of the plot. For the same experimental conditions, this proportional factor is used to determine the concentration of an unknown component from its unique peak. Determining relative contents of Si and Ge in Si—Ge thin films (Figure 9.38 and Figure 9.39) is an example of quantitative analysis of a Raman spectrum. 

The residence time for retinol in the test subject was predicted by the compartmental model to be 474 days. The residence time of 474 days is in excellent agreement with the 460 day MST that can be calculated from the data of Song et al. (1995) using the enrichment ratio method (Cobelli and Saccomani, 1992). Also, an MST of 105 to 337 days can be calculated from the half-life values (75 to 241 days) of body vitamin A reported by Sauber-lich et al. (1974) who depleted human subjects with vitamin A-deficient diets. At the same time the empirical description predicted the MST for retinol to be 26 days. While the reason for such a large discrepancy in MST (474 versus 26 days) between the compartmental model and the empirical description prediction is unclear, it is not likely to be accounted for by slight errors in estimating the final slope of the plasma retinol-d4 decay curve. Because the compartmental model embodies several features of retinol metabolism de novo production and release of retinol can occur in unobservable compartments, etc.) in addition to plasma retinol concentrations, its predicted MST is more likely to better reflect the dynamics of retinol metabolism. 

N (which is even rather small in the case of the EE technique) and one has to apply sophisticated finite-size scaling schemes. One of the simplest techniques is the so-called successive slopes method, in which the local slope of the quantity of interest versus N (usually plotted in log-log scale) is obtained numerically and plotted versus 1/N. The thermodyuamic limit is then determined as the limit of 1/N -i- 0. For excunples of the successive slopes method see Figs. 3, 4, 7, 8, and 14. More elaborated methods are the ratio method and Fade and differential approximants [36-38]. 

In the mole ratio method, the concentration of the [host] is kept constant while the concentration of [pyrene] is varied, and the absorbance of the system versus the molar ratio [pyrene]/[host] is plotted. An abrupt change in the slope will correspond to the stoichiometric ratio. With this method, the absorption of the complex is proportional to its concentration (Beer-Lambert law) thus, selecting the value of absorbance at offers the highest precision, although... 

The classic bioassay procedure which measures the animal growth response as a function of graded amounts of the missing nutrient in an otherwise complete diet and using the slope-ratio technique for evaluation is theoretically the soundest method for determining the biological availability of essential nutrients such as vitamins and indispensable amino acids. Lysine and methionine are the two amino acids for which detailed bioassay procedures have been... 

The most accurate method of deriving from /igobs. is to use the equation k ih. = /i2obs.(i+/) the ionisation ratio of the compound under study being determined directly at the required acidity and temperature. In the cases where the temperature at which rates are measured is not 25 °C the way in which Aafb. depends upon acidity will be given correctly, but again there will remain the difficulty that the slope to be expected at this temperature other than 25 °C is not known. 

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